from __future__ import print_function

import sys
'''
Dynamic Programming
Implementation of Matrix Chain Multiplication
Time Complexity: O(n^3)
Space Complexity: O(n^2)
'''
def MatrixChainOrder(array):
    N=len(array)
    Matrix=[[0 for x in range(N)] for x in range(N)]
    Sol=[[0 for x in range(N)] for x in range(N)]

    for ChainLength in range(2,N):
        for a in range(1,N-ChainLength+1):
            b = a+ChainLength-1

            Matrix[a][b] = sys.maxsize
            for c in range(a , b):
                cost = Matrix[a][c] + Matrix[c+1][b] + array[a-1]*array[c]*array[b]
                if cost < Matrix[a][b]:
                    Matrix[a][b] = cost
                    Sol[a][b] = c
    return Matrix , Sol
#Print order of matrix with Ai as Matrix
def PrintOptimalSolution(OptimalSolution,i,j):
    if i==j:
        print("A" + str(i),end = " ")
    else:
        print("(",end = " ")
        PrintOptimalSolution(OptimalSolution,i,OptimalSolution[i][j])
        PrintOptimalSolution(OptimalSolution,OptimalSolution[i][j]+1,j)
        print(")",end = " ")

def main():
    array=[30,35,15,5,10,20,25]
    n=len(array)
    #Size of matrix created from above array will be
    # 30*35 35*15 15*5 5*10 10*20 20*25
    Matrix , OptimalSolution = MatrixChainOrder(array)

    print("No. of Operation required: "+str((Matrix[1][n-1])))
    PrintOptimalSolution(OptimalSolution,1,n-1)
if __name__ == '__main__':
    main()
